LONDON—Six months ago, one of OPEC's concerns was whether a U.S. shale boom might upend crude markets by providing too much oil. Today, the group of some of the world's largest producers has a more short-term worry: How to compensate for lost Libyan crude at a time of rising demand and tensions between Russia and the West.

"That's the big question: Who will fill the gap left by Libya?" said one delegate within the group, which meets in Vienna later this week to discuss its output. Members of the Organization of...